What are the divisors of 2044?

1, 2, 4, 7, 14, 28, 73, 146, 292, 511, 1022, 2044

There is a total of 12 positive divisors.
The sum of these divisors is 4144.
The arithmetic mean is 345.33333333333.

8 even divisors

2, 4, 14, 28, 146, 292, 1022, 2044

4 odd divisors

1, 7, 73, 511

How to compute the divisors of 2044?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2044 by each of the numbers from 1 to 2044 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2044 / 1 = 2044 (the remainder is 0, so 1 is a divisor of 2044)
2044 / 2 = 1022 (the remainder is 0, so 2 is a divisor of 2044)
2044 / 3 = 681.33333333333 (the remainder is 1, so 3 is not a divisor of 2044)
...
2044 / 2043 = 1.0004894762604 (the remainder is 1, so 2043 is not a divisor of 2044)
2044 / 2044 = 1 (the remainder is 0, so 2044 is a divisor of 2044)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2044 (i.e. 45.210618221829). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2044 / 1 = 2044 (the remainder is 0, so 1 and 2044 are divisors of 2044)
2044 / 2 = 1022 (the remainder is 0, so 2 and 1022 are divisors of 2044)
2044 / 3 = 681.33333333333 (the remainder is 1, so 3 is not a divisor of 2044)
...
2044 / 44 = 46.454545454545 (the remainder is 20, so 44 is not a divisor of 2044)
2044 / 45 = 45.422222222222 (the remainder is 19, so 45 is not a divisor of 2044)